The method of multiple scales is applied to the problem of the propagation of internal equatorial Yanai and Kelvin waves through shear. Analytic formulas for the various wave fields are obtained, and the role of dissipation and the behavior of momentum and energy fluxes are investigated. Results are compared with both numerical calculations and with observations. From the latter, we are able to estimate the dissipative time scale in the tropical stratosphere. On the basis of the above findings, the Lindzen-Holton model of the quasi-biennial oscillation is modified. Abstract The method of multiple scales is applied to the problem of the propagation of internal equatorial Yanai and Kelvin waves through shear. Analytic formulas for the various wave fields are obtained, and the role of dissipation and the behavior of momentum and energy fluxes are investigated. Results are compared with both numerical calculations and with observations. From the latter, we are able to estimate the dissipative time scale in the tropical stratosphere. On the basis of the above findings, the Lindzen-Holton model of the quasi-biennial oscillation is modified.